# The insulation resistance of a 20 km long underground cable is 8 mega ohm. Insulation resistance for similar cable of 10 km is

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The insulation resistance of a 20 km long underground cable is 8 mega ohm. Insulation resistance for similar cable of 10 km is
1. 16 megaohm
2. 32 megaohm
3. 4 megaohm
4. 2 megaohm

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Correct Answer - Option 1 : 16 megaohm

Concept:

Insulation resistance is inversely proportional to length of the cable

$R = \frac{\rho }{{2\pi l}}\log \frac{{{r_2}}}{{{r_1}}}$

$\Rightarrow R \propto \frac{1}{l}$

where,

r1 = radius of core conductor,

l = length of cable

Calculation:

l1 = 20 km, R1 = 8 MΩ, l2 = 10 km

$\Rightarrow \frac{{{R_1}}}{{{R_2}}} = \frac{{{l_2}}}{{{l_1}}}$

$\Rightarrow \frac{{8 }}{{{R_2}}} = \frac{10}{20} \Rightarrow {R_2} = 16\;M{\rm{Ω }}$